Lecture 3 — The nature of unity

It is necessary to inquire how unity is related to the substance and nature of things. In a sense, this is a problem which we have examined (1001a4) in the questions regarding the nature of unity, and how it must be taken: whether it must be taken to be a substance (as the Pythagoreans first claimed, and later Plato), or rather whether there is some nature that underlies it. And it is necessary to describe it more meaningfully and more in the terms of those who speak of nature. For one of them said that unity is friendship, another air, and another the indeterminate.

If, then, it is impossible for a universal to be a substance, as has been stated in our treatment of substance and being (1038b8), and being itself cannot be a substance in the sense of one thing existing apart from the many (for it is common to all of them), but it is only a predicate, it is evident that unity cannot be a substance; for being and unity are the most universal of all predicates. Hence genera are not certain natures and substances which are separable from other things, and unity cannot be a genus, for the same reasons that being and substance cannot be such (998b17).

Further, the same thing must be true of unity in all categories of things. Now, unity and being are used in an equal number of ways.

Hence, since in the category of qualities, there is something which is one and a certain nature, and since the same thing is true of quantities, it is evident that we must investigate in a general way what unity is, just as we must investigate what being is, inasmuch as it is not sufficient to say that its nature is just itself.

But, in the sphere of colors, unity is a color—white—and the other colors seem to be produced from this and from black, and black is the privation of white as darkness is of light, for it is the absence of light. If, then, all beings were colors, they would be a number. But of what? Evidently, of colors. And unity itself would be some one color, such as white. Similarly, if beings were tunes, they would be a number of minor half tones, but their substance would not be a number, and unity would be something whose substance is not unity, but a minor half tone. Similarly, if beings were sounds, they would be a number of elements, and unity would be a vowel. And if beings were rectilinear figures, there would be a number of figures, and unity would be a triangle. The same reasoning applies to the other genera.

Therefore, if, in all passions, qualities, quantities, and motions, there are numbers and unity, and if the number is a number of particular things, and the unity is a particular unity, but unity is not its substance, then the same thing must be true of substances, because the same is true of all things. It is evident, then, that, in every genus, unity is a determinate nature, and that in no case is the nature of its unity merely unity. But, just as in the case of colors the unity for which we must look is one color, in a similar fashion, in the case of substances, the unity must be one substance.

That unity and being somehow signify the same thing is evident from the fact that they have meanings corresponding to each of the categories and are contained in none of them—neither in what it is nor in what sort—but unity is related to each in the same way that being is. This is also because “one man” does not express something different from “man,” just as being does not exist apart from what it is or from quality or from quantity; and because to be one is just the same as to be a particular thing.

1961. After having shown how unity in the sense of a measure is found first in quantity and then is transferred to the other categories, here the Philosopher deals with the relationship of unity to substance, that is, whether unity constitutes the very substance of a thing. This is divided into three parts.

In the first (1053b9; [1961]), he raises the question and gives the different opinions regarding it.

In the second (1053b16; [1963]), he answers the question by showing that unity and being are not the substance of the things of which they are predicated, at if, then.

In the third (1054a13; [1974]), he compares unity with being, at that unity and being.

He accordingly first says (1053b9) that, since it has already been shown how unity in the sense of a measure belongs to quantity and to the other genera of things, it is now necessary to ask how unity relates to the substances and natures of things. This question was asked above in book 3 (1001a4; [488]), in which different problems were raised.

1962. The question is whether the very thing which is called unity is a substance, that is, something which subsists of itself, as the Pythagoreans first claimed, and as the Platonists, who followed them, later held; or rather whether there is some subsistent nature which underlies unity, in terms of which the quiddity of the thing designated as one should be more meaningfully and adequately expressed. The philosophers of nature presupposed this entity.

One of them—Empedocles—saying that unity is love, claimed that there are four material principles, the four elements, to which the active principles posited by him, love and hate, are said to be prior. And, of these, the most important is love, inasmuch as it is perfect and the principle of good things. Therefore, if the first principle is called unity, it follows, according to him, that unity is love. And this fits the case inasmuch as it indicates a certain union of the lover and the thing loved.

Another philosopher, Diogenes, who claimed that air is the principle of all things (984a5; [86]), said that unity is air.

And still another philosopher said that unity is the indeterminate—namely, Melissus, who claimed that there was one infinite and unchangeable being, as is clear in Physics 1.

1963. If, then (1053b16). Here he answers the question which was raised. He says that unity is not a subsisting substance of which one may predicate the term “one.” He proves this in two ways.

First (1053b16; [1963]), by an argument;

second (1053b24; [1967]), by a comparison, at further, the same.

He says, then, that it was proved above in book 7 (1038b8; [1572]), where he treats of being, and especially of substance, that no universal can be a substance which subsists of itself, because every universal is common to many. A universal also cannot be a subsisting substance, for otherwise it would have to be one thing apart from the many, and then it could not be common, but would be in itself a singular thing.

1964. Unity might, it is true, be said to be common in the way a cause is. But the common aspect of a universal differs from that of a cause, for a cause is not predicated of its effects, since the same thing is not the cause of itself. But a universal is common in the sense of something predicated of many things. Thus it must be in some way a one-in-many, and not something subsisting apart from them.

1965. But being and unity must be predicated of all things in the most universal and common way. Hence those things that are called being and unity are not themselves subsisting substances, as Plato maintained.

1966. From this argument, he concludes that no genera are natures and substances which subsist of themselves, as though separable from the things of which they are predicated. This too was one of the questions debated above (998b17; [432]). Yet this is not said in the sense that unity is a genus; for unity cannot be a genus for the very same reason that being cannot, since it is not predicated univocally. This is also true in the light of the other reasons given in book 3 (1001a29–1001b19; [493–501]). And for the same reason, unity and being cannot be subsisting substances.

1967. Further, the same thing (1053b24). Here he proves the same point by a comparison. He says that unity must be found in the same way in all categories of things, because being and unity are predicated in an equal number of ways of all genera. But, in each genus of things, we look for something that is one (implying that unity is not the very nature of what is said to be one), as is evident in the case of qualities and in that of quantities. It is clear, then, that in no genus is it sufficient to say that the nature of what is said to be one is just unity itself, but we must inquire what unity and being are.

1968. That it is necessary to investigate what unity is in the category of qualities and in that of quantities he makes clear by examples. He does this first in the case of colors; for we look for something which is one, such as whiteness, which is the primary color. Hence, if what is primary in each genus of things is its unity, whiteness must constitute the unity in the genus of color; and it must be in a sense the measure of the other colors, because the more perfect a thing’s color, the closer it comes to whiteness.

He shows that whiteness is the primary color by reason of the fact that intermediate colors are produced from white and from black, and are therefore subsequent. Black is subsequent to white because it is the privation of white as darkness is of light. But this must not be understood to mean that black is pure privation in the same way that darkness is (for black is a species of color, and thus possesses the nature of color), but that blackness contains the least amount of light, which causes colors; thus it is compared to white as the absence of light is compared to light.

1969. And because, in colors, we look for something that is first and one (namely, white), it is clear that, if all beings were colors, they would have some number; not in the sense, however, that number would constitute subsisting things themselves, but in the sense that there would be a number of subsisting things of a particular sort, that is, colors. And then there would be something that is the subject of unity, namely, that which is white.

1970. The same thing would be true if all things were melodies, because beings would be of a certain number, that is, a number of minor half tones or tones. Yet number is not the very substance of beings, and consequently it would be necessary to look for something which is one, namely, the minor half tone; but not in such a way that unity itself would be a substance.

1971. Similarly, if all beings were sounds, they would be a number of beings, because there are a number of particular subjects of number, namely, of elements, or letters. Hence the vowel, which is the primary letter (since consonants cannot be pronounced without vowels) would constitute their unity. And in a similar way, if all figures were rectilinear figures, there would be a number of subjects (namely, figures), and the triangle, which is the primary rectilinear figure, would constitute their unity. For all such figures are reducible to the triangle. The same reasoning applies to every category.

1972. If it is in this way, then, that number and unity are found in all other categories—in passions, qualities, quantities, and motion—and if number and unity are not the substance of the things of which they are predicated, but number is predicated of certain substances, and if unity similarly requires some subject which is said to be one, then the same thing must be true of substances, because being and unity are predicated in the same way of all things. It is evident, then, that, in any category of things, there is some nature of which the term “one” is predicated not because unity itself is the nature of a thing, but because it is predicated of it.

1973. And just as, when we speak of unity in the case of colors, we are looking for some color which is said to be one, so too, when we speak of unity in the case of substances, we are looking for some substance of which unity may be predicated. And this is predicated primarily and chiefly of what is first among substances (which he investigates below [2553–66]), and subsequently of the other genera of things.

1974. That unity and being (1054a13). Since he had given the same argument for being and for unity, he now shows that unity and being somehow signify the same thing. He says somehow because unity and being are the same in their subject and differ only in meaning. For unity adds to being the note of undividedness, because what is one is said to be an indivisible or undivided being. He gives three reasons why unity signifies the same thing as being.

1975. The first is that unity naturally belongs to all of the different categories and not just to one of them; that is, it does not pertain just to substance or to quantity or to any other category. The same thing is also true of being.

1976. The second reason is that, when a man is said to be one, the term “one” does not express a different nature from man, just as “being” does not express a different nature from the ten categories. For if it did express a different nature, an infinite regress would necessarily result, since that nature too would be said to be one and a being. And if being were to express a nature different from these things, an infinite regress would also follow; but if not, then the conclusion of this argument must be the same as that of the first one.

1977. The third reason is that everything is said to be one inasmuch as it is a being. Hence, when a thing is dissolved, it is reduced to non-being.

1978. Now, in this solution of the question, the Philosopher seems to contradict himself, for he first said that unity and being are not the substance of the things of which they are predicated, but here he says that unity and being do not express a nature different from the things of which they are predicated.

1979. Hence it must be noted that the term “substance” is used in two senses.

In one sense, it means a suppositum in the genus of substance—which is called “first substance” and “hypostasis”—to which it properly belongs to subsist.

In a second sense, it means a thing’s quiddity, which is also referred to as a thing’s nature.

Therefore, since universals are subsistent things according to the opinion of Plato, they signify substance not only in the second sense but also in the first. But Aristotle proves in book 7 [1572] that universals are not subsistent things, and therefore it follows that universals are not substances in the first sense, but only in the second. And for this reason, it is said in the Categories that second substances, which are genera and species, do not signify particular things, which are subsisting substances, but they signify what sort of thing it is, that is, a certain nature in the genus of substance.

1980. The Philosopher accordingly proved above that unity and being do not signify substance in the sense of this particular thing, but it is necessary to look for something that is one and a being, just as we look for something that is a man or an animal, as Socrates or Plato. Later, he shows that these terms signify the natures of the things of which they are predicated, and not something added, like accidents. For common attributes differ from accidents in this respect (although they agree in not being particular things), that common attributes signify the very nature of supposita, whereas accidents do not, but they signify some added nature.

1981. And Avicenna, who did not take this into account, claimed that unity and being are accidental predicates, and that they signify a nature added to the things of which they are predicated. For he was deceived by the equivocal use of the term “one,” because the unity which is the principle of number and has the role of a measure in the genus of quantity signifies a nature added to the things of which it is predicated, since it belongs to a genus of accident. But the unity which is interchangeable with being extends to everything that is, and therefore it does not signify a nature which is limited to one category.

1982. He was also deceived by the equivocal use of the term “being”; for being as signifying the composition of a proposition is predicated accidentally, since composition is made by the intellect with regard to a definite time. Now, to exist at this or at that particular time is to be an accidental predicate. But being as divided by the ten categories signifies the very nature of the ten categories insofar as they are actual or potential.